> You use the term "white noise" as though it has
> some precise mathematical definition.
> I think it is usually used just to mean a noise
> in which no pattern can be discerned.
A white noise signal has a fourier transform of
a constant value. In other words, it's flat in the
frequency domain. In other other words, it's
got the same energy content in the same frequency
interval at all frequencies.
For example, the energy content between 10Hz and 20Hz
will be the same as the energy content between
10000Hz and 10010Hz.
(Contrast this with pink noise, where the energy between
10Hz and 20Hz, is the same as that between 1000Hz and
2000Hz and between 2000Hz and 4000Hz, etc. Pink noise
it a bit more pleasant to listen to...)
It's not mathematically obvious to me that a flat
frequency spectrum implies a completely random signal,
but it does seem likely. Is the Fourier Transform
one-to-one? If so, then there is only one possible
function that could have transform to a constant value.
Does that function have to be random?
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